Published

2010-09-01

Implementing FEM-DtN for an incompressible material on an unbounded domain

Implementación MEF-DtN para un material incompresible en un dominio no acotadoaImplementación MEF-DtN para un material incompresible en un dominio no acotado

DOI:

https://doi.org/10.15446/ing.investig.v30n3.18184

Keywords:

mixed finite element method, Taylor-Hood element, DtN technique, linear elasticity, inf-sup condition (en)
método de elementos finitos mixto, elemento Taylor-Hood, técnica DtN, elasticidad lineal, condición infsup (es)

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Authors

  • Liliana Camargo Universidad del Valle
  • Jairo Duque Universidad del Valle

This paper presents the implementation of the finite element method combined with Dirichlet-to-Neumann (DtN) mapping (derived in terms of an infinite Fourier series) for studying the solvability of an exterior problem arising in linear incomepressible 2D-elasticity. A reliable numerical experiment is also presented showing the accuracy of DtN mapping; only a few Fourier series terms were needed to get a good approximation to the solution. The stable Taylor-Hood element was used for finite element discretisation.

En este trabajo presentamos la implementación de un método de elementos finitos combinado con la aplicación Dirichlet-to-Neumann (DtN), obtenida en términos de series de Fourier, para estudiar la existencia de soluciones de un problema exterior que proviene de la teoría de elasticidad lineal incompresible bidimensional. Finalmente, se presenta un método numérico que demuestra la precisión de nuestra aplicación DtN, puesto que sólo se necesitan unos cuantos términos de la serie de Fourier para obtener una buena aproximación de la solución. Para la discretización del problema se emplea el elemento estable Taylor-Hood.

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References

Brezzi F., Fortin M., Mixed and hybrid finite element methods., Springer-Verlag, 1991.

Camargo, L., Aplicación D†N-FEM a un problema elástico lineal., BSc Mathematics thesis, Universidad del Valle, 2008.

Gatica G. N., Gatica L. F., Stephan E. P., A FEM–DtN formulation for a non-linear exterior problem in incompressible elasticity., Mathematical Methods in the Applied sciences, 26, 2003, pp. 151–170.

Han H., Bao W., The artificial boundary conditions for incompressible materials on an unbounded domain., Numerische Mathematik, 1997.

Kako T., Touda K., Numerical simulation of voice generation based on finite element method in unbounded region., Department of computer science, Japan, 2004.

Necas, J. Introduction to the theory of nonlinear elliptic equations., John Wiley & Sons, 1986.

Necas, J., Hlavacek, I., Mathematical theory of elastic and elastoplastic bodies: an introduction., Elsevier scientific publishing company, 1981.

Zeidler, E., Nonlinear functional analysis and its applications IV., Springer-Verlag, New York, 1988.

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Copyright (c) 2010 Liliana Camargo, Jairo Duque

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